Question

find the smallest number by which 8788 must be multiplied to be option a perfect cube​

Answer 1

Answer:

The required number is 2.

SOLUTION

To find the smallest number by which 8788 must be multiplied to be obtain a perfect cube​ , first let us perform prime - factorization of 8788.

$\implies$  8788 = 2 × 2 × 13 × 13 × 13

We know that , in the process of obtaining the cube of a number we group the factors into a group of three numbers.

Here,

We can group only 13 into group of three but one more 2 is need to make 2 into a group of three.

$\implies$ The smallest number by which 8788 must be multiplied to be option a perfect cube​ is 2.

LET US CHECK

Let us multiply 8788 by 2.

$\implies$ 8788 × 2 = 17576

17576 = 2 × 2 × 2 × 13 × 13 × 13

On grouping ,

17576 = 2 × 2 × 2 × 13 × 13 × 13

$\implies$ ∛ 17576 = 2 × 13 = 26.

Hence, Our answer is correct the required number is 2.